Promising M2CO2/MoX2 (M = Hf, Zr; X = S, Se, Te) Heterostructures for Multifunctional Solar Energy Applications

Two-dimensional van der Waals (vdW) heterostructures are potential candidates for clean energy conversion materials to address the global energy crisis and environmental issues. In this work, we have comprehensively studied the geometrical, electronic, and optical properties of M2CO2/MoX2 (M = Hf, Zr; X = S, Se, Te) vdW heterostructures, as well as their applications in the fields of photocatalytic and photovoltaic using density functional theory calculations. The lattice dynamic and thermal stabilities of designed M2CO2/MoX2 heterostructures are confirmed. Interestingly, all the M2CO2/MoX2 heterostructures exhibit intrinsic type-II band structure features, which effectively inhibit the electron-hole pair recombination and enhance the photocatalytic performance. Furthermore, the internal built-in electric field and high anisotropic carrier mobility can separate the photo-generated carriers efficiently. It is noted that M2CO2/MoX2 heterostructures exhibit suitable band gaps in comparison to the M2CO2 and MoX2 monolayers, which enhance the optical-harvesting abilities in the visible and ultraviolet light zones. Zr2CO2/MoSe2 and Hf2CO2/MoSe2 heterostructures possess suitable band edge positions to provide the competent driving force for water splitting as photocatalysts. In addition, Hf2CO2/MoS2 and Zr2CO2/MoS2 heterostructures deliver a power conversion efficiency of 19.75% and 17.13% for solar cell applications, respectively. These results pave the way for exploring efficient MXenes/TMDCs vdW heterostructures as photocatalytic and photovoltaic materials.


Introduction
The production of sustainable and renewable energy can effectively tackle both the increasing global energy demand and environmental pollution issues [1]. Harnessing solar energy via photocatalytic hydrogen productions and photovoltaic solar cells have been proposed as promising solutions, which optimize the utilization of solar energy in a cost-effective and efficient way [2][3][4]. The search for efficient photocatalytic and photovoltaic materials is one of the most daunting tasks in the use of solar energy nowadays. Since graphene has been successfully produced and applied [5][6][7][8], great attention has been paid to 2D materials, for instance, transition metal carbides/nitrides (MXenes) [9][10][11], carbonitrides [12] transition metal dichalcogenides (TMDCs) [13][14][15], black phosphorene [16] and silicene [17]. Herein, MXenes, first successfully divested from the MAX phase in 2011 [18,19], can be expressed by M n+1 X n T x (n = 1~3), in which M is early transition metals, X refers to carbon or nitrogen, and T indicates surface terminations, such as hydroxyl groups, oxygen, or fluorine [10,20]. Usually, the functionalization of the MXenes surface makes the modulation of electronic properties more efficient [21,22], which enhances the possibility of solar energy-related applications [23][24][25][26].
On the other hand, the structural formula of TMDCs is generally expressed as MX 2 , where M refers to the transition metal elements (W, Mo, Re, etc.), and X represents the elements (S, Se, and Te). TMDCs materials exhibit a similar three-layer structure, where a transition metal atom single layer is sandwiched between two hexagonal chalcogenide atom planes. TMDCs have garnered significant interest owing to their emergent properties in the realm of light-emitting and photonic devices [27][28][29]. Among the TMDCs family, MoS 2 , MoSe 2, and MoTe 2 stand out with their distinguished physical and chemical properties, such as good stability, flexibility, electronic conductivity, optical, and catalytic properties [30][31][32][33]. However, the applications of transition metal dichalcogenides (TMDCs) in photocatalytic and photovoltaic applications are hindered by limitations such as inadequate spatial separation of electron-hole pairs, substantial photo-corrosion, and high light transmittance [34]. Consequently, a promising approach to enhance electron-hole separation in TMDCs is the construction of heterostructures with 2D semiconducting materials.
To further enhance the properties of 2D materials, vdW heterostructures with weak vdW interactions between vertical layers have been proposed [35,36]. Based on the interlayer coupling effect, 2D vertical vdW heterostructures exhibit distinct advantages derived from each constituent material, thereby yielding unique and promising features [37,38]. MXenes and TMDCs are potential candidates to form vdW heterostructures. For instance, MoSe 2 /Ti 3 C 2 [39] and MoSe 2 /Ti 3 C 2 O 2 [40] integrate the properties of their individual components, which show potential applications in photocatalysis, photovoltaics, and optoelectronics. The abundance and possibilities of combining MXenes and TMDCs together promote the investigation of MXene/TMDC vdW heterostructures of general interest and great importance. It is worth noting that the oxygen-functionalized MXenes materials Hf 2 CO 2 and Zr 2 CO 2 possess suitable band gaps for solar energy harvesting applications. The construction of heterostructures using M 2 CO 2 (M = Hf, Zr) and TMDCs MoX 2 (X = S, Se, Te) with the same hexagonal 2D lattice and restricted lattice mismatch not only serves as a remedy for the aforementioned drawbacks of MoX 2 materials but also exhibits significant potential for optoelectronic and photocatalytic applications.
In this work, we constructed the M 2 CO 2 /MoX 2 (M = Hf, Zr; X = S, Se, Te) heterostructures to investigate their photocatalytic hydrolysis and photoelectric conversion mechanism to evaluate the potential in photocatalytic and photovoltaic applications. Using first-principles calculations, we performed a comprehensive study on the structural stability, electronic structure, photocatalytic mechanism, and optoelectronic properties of M 2 CO 2 /MoX 2 heterostructures. Interestingly, the Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures have the potential for promising candidates for overall water splitting, owing to their band gaps and band edge positions that are suitable for photocatalytic water splitting. Moreover, the estimated maximum power conversion efficiencies of Hf 2 CO 2 /MoS 2 and Zr 2 CO 2 /MoS 2 heterostructures are pretty excellent and are considerably competitive with other existing heterostructures. These findings will diversify catalyst options of MXenes/TMDCs vdW heterostructures for photocatalytic hydrogen production and solar cell energy storage.

Computational Details
Our density functional theory (DFT) calculations were performed by using the VASP package [41] together with the ALKEMIE platform [42,43]. The exchange-correlation interactions between electrons were carried out using the projector-augmented wave (PAW) [44] generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional [45]. The cutoff energy for the plane-wave-basis was set to 500 eV. For both geometry optimization and electronic structure calculation, the 2D Brillouin zone was installed with a Γ-centered k point of 12 × 12 × 1 mesh. To eliminate the interactions of periodic twolayer adjacent heterostructures, a vacuum layer larger than 20 Å was added along the z-direction of the 2D models. To have the assurance that the heterogeneous structures were fully optimized, the precision energy and precision force were required to be within 10 −5 eV and 0.01 eV/Å, respectively. The Grimme's DFT-D3 method was used to include the long-range vdW interactions [46,47]. The HSE06 hybrid density was functional and was utilized for the precise determination of bandgap values [48]. To verify the lattice dynamic stability of heterostructures, the phono dispersion curves were calculated using Phonopy code [49] with a 3 × 3 × 1 supercell. In order to investigate the thermodynamic stability of M 2 CO 2 /MoX 2 heterostructures at room temperature (300 K), ab initio molecular dynamics (AIMD) simulations were performed with a supercell of size 3 × 3 × 1 [50,51].

Data Analysis
To quantify the lattice constant differences between different 2D structures, the degree of lattice mismatch K is defined in the theoretical calculation of heterostructures as [52]: where a 1 and a 2 are the lattice constants of the two monolayers forming the heterostructures.
To examine the thermodynamic stabilities of 2D heterostructures, the formation energy E f is obtained according to [53]: where E M 2 CO 2 /MoX 2 is the total energy of the M 2 CO 2 /MoX 2 heterostructures, E M 2 CO 2 and E MoX 2 are the total energies of pristine M 2 CO 2 and MoX 2 monolayers, respectively. On the other hand, we have also calculated the 2D heterostructure binding energy E b to assess the strength of vdW interactions according to: where E h M 2 CO 2 /MoX 2 is the sum of the total energies of M 2 CO 2 and MoX 2 monolayers fixed in the corresponding heterostructure lattice, and S h represents the 2D unit cell area. The absorption coefficients of 2D materials α(ω) are derived from [54]: where ε 1 and ε 2 are the real and imaginary parts of the optical dielectric functions, respectively. The carrier mobility of 2D materials µ was calculated by [55]: where e, , C 2D , K B , T, m * and E 1 are the electron charge, reduced Planck constant, 2D elastic modulus, Boltzmann constant, temperature, carrier effective mass, and deformation potential constant, respectively.
Furthermore, by perpendicularly combining the monolayers, M 2 CO 2 /MoX 2 (M = Hf, Zr; X = S, Se, Te) heterostructures were built. The lattice mismatches observed between the M 2 CO 2 and MoX 2 monolayers fall within the reasonable range from 0.1% to 7.9%, which indicates the feasibility of establishing M 2 CO 2 /MoX 2 heterostructures. Herein, to investigate the stability of M 2 CO 2 /MoX 2 heterostructures, six distinct stacking configurations were examined. Taking Zr 2 CO 2 /MoS 2 as an example, Figure 1 displays the top and side views of the diverse stacking structures examined, and Table S2 presents the respective calculated total energies. Details of the most stable structures after structural optimization under the van der Waals correction algorithm are presented in Table S3. It is noted that stacking II is the most stable model for most systems. The only exception is that stacking IV is the most stable configuration for Hf 2 CO 2 /MoTe 2 heterostructure. In the following, the most stable stacking configurations were used for further electronic structure calculations. The formation energies presented in Table S3 demonstrate the energetic favorability of these heterostructures, as evidenced by their negative or minimally positive values [64]. Additionally, all heterostructures are classical van der Waals heterostructures, whose optimized interlayer distances and binding energy are around 3 Å and −20 meV/Å 2 [65], respectively. Moreover, the negative binding energy corresponds to the exothermic reaction, which further confirms the feasibility from the thermodynamics point of view.
Furthermore, by perpendicularly combining the monolayers, M2CO2/MoX2 (M = Hf, Zr; X = S, Se, Te) heterostructures were built. The lattice mismatches observed between the M2CO2 and MoX2 monolayers fall within the reasonable range from 0.1% to 7.9%, which indicates the feasibility of establishing M2CO2/MoX2 heterostructures. Herein, to investigate the stability of M2CO2/MoX2 heterostructures, six distinct stacking configurations were examined. Taking Zr2CO2/MoS2 as an example, Figure 1 displays the top and side views of the diverse stacking structures examined, and Table S2 presents the respective calculated total energies. Details of the most stable structures after structural optimization under the van der Waals correction algorithm are presented in Table S3. It is noted that stacking II is the most stable model for most systems. The only exception is that stacking IV is the most stable configuration for Hf2CO2/MoTe2 heterostructure. In the following, the most stable stacking configurations were used for further electronic structure calculations. The formation energies presented in Table S3 demonstrate the energetic favorability of these heterostructures, as evidenced by their negative or minimally positive values [64]. Additionally, all heterostructures are classical van der Waals heterostructures, whose optimized interlayer distances and binding energy are around 3 Å and −20 meV/Å 2 [65], respectively. Moreover, the negative binding energy corresponds to the exothermic reaction, which further confirms the feasibility from the thermodynamics point of view. In order to further confirm the dynamic and thermal stabilities of the M2CO2/MoX2 heterostructures, we performed phonon dispersion calculations and AIMD simulations. For one thing, Figure 2 illustrates the phonon dispersion curves for the M2CO2/MoX2 heterostructures. Owing to the existence of eight atoms within each unit cell of the heterostructure, a total of 24 spectral lines are generated in Figure 2, encompassing 21 In order to further confirm the dynamic and thermal stabilities of the M 2 CO 2 /MoX 2 heterostructures, we performed phonon dispersion calculations and AIMD simulations. For one thing, Figure 2 illustrates the phonon dispersion curves for the M 2 CO 2 /MoX 2 heterostructures. Owing to the existence of eight atoms within each unit cell of the heterostructure, a total of 24 spectral lines are generated in Figure 2, encompassing 21 optical modes and 3 acoustic modes. Furthermore, minimal imaginary frequencies are observed from the phonon dispersion curves, which could be eliminated by depositing the M 2 CO 2 /MoX 2 heterostructures onto suitable substrates or applying slight strain [66,67]. For another, it can be seen from the energy and structure evolutions in Figure 3 that total energies change in small ranges with temperature and atoms vibrate only slightly around the equilibrium position after a simulation time of 9 ps. Overall, M 2 CO 2 /MoX 2 vdW heterostructures show good lattice dynamic and thermal dynamic stabilities. observed from the phonon dispersion curves, which could be eliminated by depositing the M2CO2/MoX2 heterostructures onto suitable substrates or applying slight strain [66,67]. For another, it can be seen from the energy and structure evolutions in Figure 3 that total energies change in small ranges with temperature and atoms vibrate only slightly around the equilibrium position after a simulation time of 9 ps. Overall, M2CO2/MoX2 vdW heterostructures show good lattice dynamic and thermal dynamic stabilities.  To gain a more comprehensive comprehension of the electronic structures, the projected HSE06 band structures of the M2CO2/MoX2 heterostructures are illustrated in Figure 4. It can be seen that Hf2CO2/MoTe2 and Zr2CO2/MoTe2 show direct band gap observed from the phonon dispersion curves, which could be eliminated by depositing the M2CO2/MoX2 heterostructures onto suitable substrates or applying slight strain [66,67]. For another, it can be seen from the energy and structure evolutions in Figure 3 that total energies change in small ranges with temperature and atoms vibrate only slightly around the equilibrium position after a simulation time of 9 ps. Overall, M2CO2/MoX2 vdW heterostructures show good lattice dynamic and thermal dynamic stabilities.  To gain a more comprehensive comprehension of the electronic structures, the projected HSE06 band structures of the M2CO2/MoX2 heterostructures are illustrated in Figure 4. It can be seen that Hf2CO2/MoTe2 and Zr2CO2/MoTe2 show direct band gap To gain a more comprehensive comprehension of the electronic structures, the projected HSE06 band structures of the M 2 CO 2 /MoX 2 heterostructures are illustrated in Figure 4. It can be seen that Hf 2 CO 2 /MoTe 2 and Zr 2 CO 2 /MoTe 2 show direct band gap structures, where both VBM and CBM locate at the M point. On the other hand, the other heterostructures present indirect band gap features. Table S4 lists the calculated band gaps of the most stable configurations for M 2 CO 2 /MoX 2 heterostructures. As listed in Tables S1 and S4, the band gaps of Hf 2 CO 2 /MoS 2 , Hf 2 CO 2 /MoSe 2 , Hf 2 CO 2 /MoTe 2 , Zr 2 CO 2 /MoS 2, Zr 2 CO 2 /MoSe 2 and Zr 2 CO 2 /MoTe 2 heterostructures are comparatively lower than those of their corresponding monolayers, with values of 1.35, 1.64, 0.66, 1.11, 1.69, and 1.13 eV, respectively. This observation indicates that the electron can be excited and more accessible with less light energy. In Hf 2 CO 2 /MoS 2 and Zr 2 CO 2 /MoS 2 heterostructures, the VBM are primarily influenced by the contribution of the M 2 CO 2 layers, while the CBM are predominantly determined by the MoX 2 layers. In contrast, the VBM and CBM are dominated by MoX 2 and M 2 CO 2 monolayers in the other heterostructures, respectively. Interestingly, all the M 2 CO 2 /MoX 2 heterostructures are categorized as type-II heterostructures, which enables the effective separation of photo-generated charge carriers [36].
gaps of the most stable configurations for M2CO2/MoX2 heterostructures. As listed in Tables S1 and S4, the band gaps of Hf2CO2/MoS2, Hf2CO2/MoSe2, Hf2CO2/MoTe2, Zr2CO2/MoS2, Zr2CO2/MoSe2 and Zr2CO2/MoTe2 heterostructures are comparatively lower than those of their corresponding monolayers, with values of 1.35, 1.64, 0.66, 1.11, 1.69, and 1.13 eV, respectively. This observation indicates that the electron can be excited and more accessible with less light energy. In Hf2CO2/MoS2 and Zr2CO2/MoS2 heterostructures, the VBM are primarily influenced by the contribution of the M2CO2 layers, while the CBM are predominantly determined by the MoX2 layers. In contrast, the VBM and CBM are dominated by MoX2 and M2CO2 monolayers in the other heterostructures, respectively. Interestingly, all the M2CO2/MoX2 heterostructures are categorized as type-II heterostructures, which enables the effective separation of photo-generated charge carriers [36]. To further explore the charge transfer between M2CO2 and MoX2 monolayers, the charge density difference   can be calculated from the following [68]: where the   The charge transfer contributes to the formation of built-in electric fields between the monolayers, which drives the photogenerated electrons and holes in opposite directions and further promotes the separation of electrons from holes [69]. It has been observed that the degree of charge transfer between layers exhibits a strong correlation with photocatalytic and photovoltaic To further explore the charge transfer between M 2 CO 2 and MoX 2 monolayers, the charge density difference ∆ρ can be calculated from the following [68]: where the ρ M 2 CO 2 /MoX 2 , ρ M 2 CO 2 , and ρ MoX 2 are the charge densities of the M 2 CO 2 /MoX 2 heterostructures, M 2 CO 2 and MoX 2 monolayers, respectively. The 3D iso-surface and planar average of the charge difference densities along the z-direction are illustrated in Figure 5. Except for Zr 2 CO 2 /MoS 2 heterostructure, the charges consume in the MoX 2 sides and accumulate in the M 2 CO 2 regions. From the Bader charge analysis listed in Table S5, we found that 0.0066, 0.0104, 0.0157, 0.0094, and 0.0197 electrons transfer from MoX 2 to M 2 CO 2 slabs in the Hf 2 CO 2 /MoS 2 , Hf 2 CO 2 /MoSe 2 , Hf 2 CO 2 /MoTe 2 , Zr 2 CO 2 /MoSe 2, and Zr 2 CO 2 /MoTe 2 heterostructures, respectively. On the contrary, for Zr 2 CO 2 /MoS 2 , there are 0.0158 electrons from Zr 2 CO 2 to the MoS 2 side. The charge transfer contributes to the formation of built-in electric fields between the monolayers, which drives the photogenerated electrons and holes in opposite directions and further promotes the separation of electrons from holes [69]. It has been observed that the degree of charge transfer between layers exhibits a strong correlation with photocatalytic and photovoltaic activities. The electron localization functions (ELF) further visualize the detailed chemical bonding features in M 2 CO 2 /MoX 2 heterostructures. Figure 6 presents the 2D contour plots of ELF in the (110) plane. It shows that the ELF bond points of the vdW bonding are about 0.040 for M 2 CO 2 /MoX 2 heterostructures, which confirms the vdW interaction between M 2 CO 2 and MoX 2 layers.
activities. The electron localization functions (ELF) further visualize the detailed chemical bonding features in M2CO2/MoX2 heterostructures. Figure 6 presents the 2D contour plots of ELF in the (110) plane. It shows that the ELF bond points of the vdW bonding are about 0.040 for M2CO2/MoX2 heterostructures, which confirms the vdW interaction between M2CO2 and MoX2 layers.  To understand the chemical driving force for the water-splitting reaction, the band edge alignments of the M2CO2, MoX2 monolayers, and M2CO2/MoX2 heterostructures in conjunction with the work functions were investigated, as shown in Figure 7. The energy levels of the VBM and CBM of the MoS2, MoSe2, Hf2CO2, and Zr2CO2 monolayers satisfy the requirements of the redox potential of water splitting. However, the VBM of the MoTe2 activities. The electron localization functions (ELF) further visualize the detailed chemical bonding features in M2CO2/MoX2 heterostructures. Figure 6 presents the 2D contour plots of ELF in the (110) plane. It shows that the ELF bond points of the vdW bonding are about 0.040 for M2CO2/MoX2 heterostructures, which confirms the vdW interaction between M2CO2 and MoX2 layers.  To understand the chemical driving force for the water-splitting reaction, the band edge alignments of the M2CO2, MoX2 monolayers, and M2CO2/MoX2 heterostructures in conjunction with the work functions were investigated, as shown in Figure 7. The energy levels of the VBM and CBM of the MoS2, MoSe2, Hf2CO2, and Zr2CO2 monolayers satisfy the requirements of the redox potential of water splitting. However, the VBM of the MoTe2 To understand the chemical driving force for the water-splitting reaction, the band edge alignments of the M 2 CO 2 , MoX 2 monolayers, and M 2 CO 2 /MoX 2 heterostructures in conjunction with the work functions were investigated, as shown in Figure 7. The energy levels of the VBM and CBM of the MoS 2 , MoSe 2 , Hf 2 CO 2 , and Zr 2 CO 2 monolayers satisfy the requirements of the redox potential of water splitting. However, the VBM of the MoTe 2 monolayer is higher than the oxidation-reduction potential. The result agrees well with the previous report [60]. Herein, the work functions for MoS 2 , MoSe 2 , MoTe 2 , Zr 2 CO 2, and Hf 2 CO 2 monolayers are 5.68, 5.06, 4.60, 5.23, and 5.17 eV, respectively. The disparity in the work function across monolayers contributes to the electron transfer in the vdW heterostructures until the Fermi energy level reaches equilibrium, which is beneficial to form built-in electric fields. Herein, Hf 2 CO 2 /MoSe 2 and Zr 2 CO 2 /MoSe 2 heterostructures with suitable band edge alignments for water oxidations and reductions, render them effective photocatalysts for overall water splitting. monolayer is higher than the oxidation-reduction potential. The result ag the previous report [60]. Herein, the work functions for MoS2, MoSe2, MoT Hf2CO2 monolayers are 5.68, 5.06, 4.60, 5.23, and 5.17 eV, respectively. The d work function across monolayers contributes to the electron transfer heterostructures until the Fermi energy level reaches equilibrium, which form built-in electric fields. Herein, Hf2CO2/MoSe2 and Zr2CO2/MoSe2 he with suitable band edge alignments for water oxidations and reductions effective photocatalysts for overall water splitting. To obtain the charge carrier transport characteristics, we calculat effective masses and mobilities in M2CO2/MoX2 heterostructures along directions with the orthorhombic lattices. We have rebuilt the hexago orthorhombic cell for the carrier mobility calculations, as shown in Figur Zr2CO2/MoS2 as an example. The effective masses ( * m ), deformation pote elastic modulus ( 2D C ), and carrier mobilities (  ) are summarized in Table   hand, the predicted hole mobilities of M2CO2/MoX2 heterostructures are mu the electron mobilities. On the other hand, the carrier mobilities of M2CO the characteristic of high anisotropy. Generally, electron mobilities along are greater than the y direction, and vice versa, hole mobilities along the greater than the x direction. Therefore, the electrons tend to go through the the MoX2 side, while the holes demonstrate a predilection for migration a within the M2CO2 domain of the heterostructures. Interestingly, the hol Hf2CO2/MoS2 and Hf2CO2/MoTe2 heterostructures in the y direction have re cm 2 V −1 s −1 and 7592.80 cm 2 V −1 s −1 , respectively, which are greater than silic V −1 s −1 ) [70]. The strong anisotropic carrier mobility in M2CO2/MoX2 hetero reduce the rate of electron-hole recombination, which is favorable to redox the photoelectric conversion process. To obtain the charge carrier transport characteristics, we calculated the carrier effective masses and mobilities in M 2 CO 2 /MoX 2 heterostructures along the x and y directions with the orthorhombic lattices. We have rebuilt the hexagonal cell to an orthorhombic cell for the carrier mobility calculations, as shown in Figure S2 by taking Zr 2 CO 2 /MoS 2 as an example. The effective masses (m * ), deformation potentials (E 1 ), 2D elastic modulus (C 2D ), and carrier mobilities (µ) are summarized in Table 1. On the one hand, the predicted hole mobilities of M 2 CO 2 /MoX 2 heterostructures are much larger than the electron mobilities. On the other hand, the carrier mobilities of M 2 CO 2 /MoX 2 exhibit the characteristic of high anisotropy. Generally, electron mobilities along the x direction are greater than the y direction, and vice versa, hole mobilities along the y direction are greater than the x direction. Therefore, the electrons tend to go through the x direction on the MoX 2 side, while the holes demonstrate a predilection for migration along the y-axis within the M 2 CO 2 domain of the heterostructures. Interestingly, the hole mobilities of Hf 2 CO 2 /MoS 2 and Hf 2 CO 2 /MoTe 2 heterostructures in the y direction have reached 9140.34 cm 2 V −1 s −1 and 7592.80 cm 2 V −1 s −1 , respectively, which are greater than silicon (~1400 cm 2 V −1 s −1 ) [70]. The strong anisotropic carrier mobility in M 2 CO 2 /MoX 2 heterostructures can reduce the rate of electron-hole recombination, which is favorable to redox reactions and the photoelectric conversion process. As the optical property is one of the most important indicators for considering materials in solar energy conversion applications, subsequently, we investigated the optical absorption coefficient of the M 2 CO 2 /MoX 2 vdW heterostructures. Figure 8 depicts the absorption coefficient curves of the M 2 CO 2 /MoX 2 heterostructures and the corresponding monolayers using HSE06. In general, M 2 CO 2 /MoX 2 heterostructures exhibit significant enhancement in the optical absorption coefficient (blue curves in Figure 8), featuring multiple high absorption peaks in both the visible and ultraviolet regions. The absorption coefficient of M 2 CO 2 /MoX 2 is over two-fold higher than that of M 2 CO 2 and notably exceeds that of the corresponding MoX 2 monolayers. It is worth noting that Hf 2 CO 2 /MoS 2 and Zr 2 CO 2 /MoS 2 heterostructures exhibit stronger responses to infrared light than monolayers as well. Moreover, compared to M 2 CO 2 and MoX 2 monolayers, the absorption peaks of the vdW heterostructures undergo a slight redshift due to the narrowed bandgap. Therefore, the formation of heterostructures enhances optical response, showing promising potential for M 2 CO 2 /MoX 2 heterostructures in photocatalysis and photovoltaic applications.
According to the previous analysis, Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures are ideal materials for photocatalytic water splitting. The E VBM of Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 are more positive than the redox potential of O 2 /H 2 O (1.23 eV corresponds to the potential of −5.67 eV at pH = 0), while the E CBM is more negative than the redox potential of H + /H 2 O (0 eV corresponds to the potential of −4.44 eV at pH = 0). Meanwhile, they are also type-II semiconductors, which avoid the recombination of photo-generated carriers. Therefore, to further reveal the photocatalytic mechanism, we take the Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures as examples to further analyze the adsorption and dissociation processes of water molecules on the surface of M 2 CO 2 , as presented in Figure 9a. Under light irradiation, electrons in the Zr 2 CO 2 /MoSe 2 heterostructure are excited from the valence bands to the conduction bands, while an equal amount of holes remain in the valence bands. Immediately afterward, electrons are transferred from the CBM of MoSe 2 to Zr 2 CO 2 , and holes are from the VBM of Zr 2 CO 2 to MoSe 2 , thus forming an internal electric field that effectively accelerates the electron-hole recombination. Combined with the projected band diagram, the hydrogen evolution reaction (HER) occurs on the Zr 2 CO 2 surface and the oxygen evolution reaction (OER) takes place on the MoSe 2 surface. For Hf 2 CO 2 /MoSe 2 heterostructure, the photocatalysis mechanism is the same. Here, we analyzed the HER processes on the Zr 2 CO 2 and Hf 2 CO 2 surfaces of the Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures. Based on the crystal structure features, effective adsorption sites A~C and D~F were considered on the surfaces of Zr 2 CO 2 and Hf 2 CO 2 , as shown in Figure S3. The adsorption models were subjected to complete relaxation and the adsorption energies of water molecules E H 2 O/surface ads were calculated from [71]: where E H 2 O/surface tot , E H 2 O tot and E surface tot are the total energy of the absorption system, individual water molecules, and pristine surface, respectively. Herein, the location with the lowest adsorption energy is where the HER takes place. The optimized models and the corresponding adsorption energies after water adsorption at different sites are exhibited in Figure S4 and S5. Different absorbed models obtain adsorption energies from −0.061 to −0.338 eV. All the cases with negative adsorption energies indicate that the water molecule adsorption processes are thermodynamically favorable. It is observed that the adsorption energy is lower in the case of oxygen atoms as adsorption atoms, which indicates that water molecules are more stable on the surface of the heterojunction with oxygen atoms. For the Zr 2 CO 2 and Hf 2 CO 2 surfaces, the optimal adsorption sites are C and F, where the HER will take place most possibly.   Figure S4 and S5. Different absorbed models obtain adsorption energies from −0.061 to −0.338 eV. All the cases with negative adsorption energies indicate that the water molecule adsorption processes are thermodynamically favorable. It is observed that the adsorption energy is lower in the case of oxygen atoms as adsorption atoms, which indicates that water molecules are more stable on the surface of the heterojunction with oxygen atoms. For the Zr2CO2 and Hf2CO2 surfaces, the optimal adsorption sites are C and F, where the HER will take place most possibly. Furthermore, the generation processes of H2 on the Zr2CO2 and Hf2CO2 surfaces of Zr2CO2/MoSe2 and Hf2CO2/MoSe2 heterostructures have been illustrated in Figure 9b. For Zr2CO2/MoSe2 heterostructure, the isolated H adatoms exhibit an inclination to migrate in closer proximity to one another under a chemical driving force of −0.21 eV. This driving force is termed as the energy differential between two proximal hydrogen atoms (marked as Step-I and set to 0) and two remote hydrogen atoms (marked as Step-II) on the Zr2CO2 surface. Afterward, H atoms will form H2 molecules (marked as Step-III) accompanied by a chemical driving force of −4.48 eV (from −0.21 eV of Step-II to −4.69 eV of Step-III) on the Zr2CO2 surface, while the system is less energetic and more thermodynamically stable. The generated hydrogen will be departed easily from the surface (marked as Step-IV), as only 0.12 eV energy is required (from −4.69 eV of Step-III to −4.57 eV of Step-IV). On the other hand, the process of producing H2 molecules on the Hf2CO2 surface of the Hf2CO2/MoSe2 heterostructure is similar. The energies taken for the gradual approach of two distant H atoms to form an H2 molecule and then to detach from the surface are −0.30, −6.13, and 0.08 eV, respectively.
To evaluate the application of M2CO2/MoX2 heterostructures in solar cells, we conducted an estimation of the power conversion efficiency (PCE,  ), which describes the ability of M2CO2/MoX2 heterostructure materials to transform solar energy into electrical energy, proposed by Scharber et al. [72]: (8) where 0.65 is the band-fill factor, ( )  P is the AM1.5 solar energy flux at the photon energy  , and d g E is the donor band gap.  c E is the donor and acceptor conduction band offset. To better understand the conduction band offset, Figure S6 presents the band Furthermore, the generation processes of H 2 on the Zr 2 CO 2 and Hf 2 CO 2 surfaces of Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures have been illustrated in Figure 9b. For Zr 2 CO 2 /MoSe 2 heterostructure, the isolated H adatoms exhibit an inclination to migrate in closer proximity to one another under a chemical driving force of −0.21 eV. This driving force is termed as the energy differential between two proximal hydrogen atoms (marked as Step-I and set to 0) and two remote hydrogen atoms (marked as Step-II) on the Zr 2 CO 2 surface. Afterward, H atoms will form H 2 molecules (marked as Step-III) accompanied by a chemical driving force of −4.48 eV (from −0.21 eV of Step-II to −4.69 eV of Step-III) on the Zr 2 CO 2 surface, while the system is less energetic and more thermodynamically stable. The generated hydrogen will be departed easily from the surface (marked as Step-IV), as only 0.12 eV energy is required (from −4.69 eV of Step-III to −4.57 eV of Step-IV). On the other hand, the process of producing H 2 molecules on the Hf 2 CO 2 surface of the Hf 2 CO 2 /MoSe 2 heterostructure is similar. The energies taken for the gradual approach of two distant H atoms to form an H 2 molecule and then to detach from the surface are −0.30, −6.13, and 0.08 eV, respectively.
To evaluate the application of M 2 CO 2 /MoX 2 heterostructures in solar cells, we conducted an estimation of the power conversion efficiency (PCE, η), which describes the ability of M 2 CO 2 /MoX 2 heterostructure materials to transform solar energy into electrical energy, proposed by Scharber et al. [72]: where 0.65 is the band-fill factor, P( ) is the AM1.5 solar energy flux at the photon energy , and E d g is the donor band gap. ∆E c is the donor and acceptor conduction band offset. To better understand the conduction band offset, Figure S6 presents the band structures of individual monolayers that have been arranged in the 2D lattice of the corresponding van der Waals heterostructure, based on the band edge data. The donor band gap E d g , conduction band offset ∆E c , and calculated PCE (η) of M 2 CO 2 /MoX 2 heterostructures are listed in Table S6. Figure 10 shows simulated solar cell PCE as well as the charge carrier transfer route in M 2 CO 2 /MoX 2 heterostructures. Interestingly, the maximum PCEs of the Hf 2 CO 2 /MoS 2 and Zr 2 CO 2 /MoS 2 heterostructures are calculated to be 19.75% and 17.13% (red star highlighted in Figure 10a), respectively. Remarkably, the donor band gaps of Hf 2 CO 2 /MoS 2 and Zr 2 CO 2 /MoS 2 heterostructures are in the range of the ideal band gap for the best light absorption characteristics of solar cells [73,74]. As shown in Figure 10b, photon absorptions in M 2 CO 2 /MoX 2 heterostructures with high PCEs generate excited-free carriers to develop photocurrent more efficiently.
heterostructures are listed in Table S6. Figure 10 shows simulated solar cell PCE as well as the charge carrier transfer route in M2CO2/MoX2 heterostructures. Interestingly, the maximum PCEs of the Hf2CO2/MoS2 and Zr2CO2/MoS2 heterostructures are calculated to be 19.75% and 17.13% (red star highlighted in Figure 10a), respectively. Remarkably, the donor band gaps of Hf2CO2/MoS2 and Zr2CO2/MoS2 heterostructures are in the range of the ideal band gap for the best light absorption characteristics of solar cells [73,74]. As shown in Figure 10b, photon absorptions in M2CO2/MoX2 heterostructures with high PCEs generate excited-free carriers to develop photocurrent more efficiently.

Conclusions
In conclusion, we have systematically investigated the geometrical structures, electronic structures, optical properties, photocatalytic and photovoltaic applications of M2CO2 (M = Hf, Zr), MoX2 (X = S, Se, Te) monolayers and corresponding M2CO2/MoX2 vdW heterostructures based on density functional theory calculations. Firstly, the most stable configurations of these heterostructures have been determined by the formation energy. The thermal and lattice dynamic stabilities of the M2CO2/MoX2 heterostructures are demonstrated by the negligible fluctuations of total energy and atomic equilibrium positions with temperature during ab initio molecular dynamics simulations, coupled with the scarcity of imaginary frequencies present in the phonon dispersion curves. Secondly, the calculated bandgap values of these heterostructures exhibit a reduced extent in comparison to those of the associated monolayers. It is noted Hf2CO2/MoTe2, and Zr2CO2/MoTe2 heterostructures display direct band gap characteristics, which are favorable for solar light absorption. Moreover, it is found that built-in polarization electric fields generated near the interfaces, as well as the high and anisotropic carrier mobility, can facilitate the photo-generated carrier separation to improve the photoelectric conversion process. In contrast to the M2CO2 and MoX2 monolayers, the M2CO2/MoX2 heterostructures display a heightened optical absorption effect, predominantly within the ultraviolet and visible light spectra. Interestingly, the M2CO2/MoX2 heterostructures all exhibit the intrinsic type-II semiconductors, the VBM and CBM primarily influenced by the contribution of different layers, which effectively hinder the recombination of electron-hole pairs. Lastly, the Zr2CO2/MoSe2 and Hf2CO2/MoSe2 heterostructures are considered highly prospective contenders for water splitting, given their appropriate band gaps and band edge positions that furnish ample driving force for the redox reaction of water. Furthermore, the designed Hf2CO2/MoS2 and Zr2CO2/MoS2 heterostructures can achieve PCE values of 19.75% and 17.13%, respectively. The present study reveals that

Conclusions
In conclusion, we have systematically investigated the geometrical structures, electronic structures, optical properties, photocatalytic and photovoltaic applications of M 2 CO 2 (M = Hf, Zr), MoX 2 (X = S, Se, Te) monolayers and corresponding M 2 CO 2 /MoX 2 vdW heterostructures based on density functional theory calculations. Firstly, the most stable configurations of these heterostructures have been determined by the formation energy. The thermal and lattice dynamic stabilities of the M 2 CO 2 /MoX 2 heterostructures are demonstrated by the negligible fluctuations of total energy and atomic equilibrium positions with temperature during ab initio molecular dynamics simulations, coupled with the scarcity of imaginary frequencies present in the phonon dispersion curves. Secondly, the calculated bandgap values of these heterostructures exhibit a reduced extent in comparison to those of the associated monolayers. It is noted Hf 2 CO 2 /MoTe 2 , and Zr 2 CO 2 /MoTe 2 heterostructures display direct band gap characteristics, which are favorable for solar light absorption. Moreover, it is found that built-in polarization electric fields generated near the interfaces, as well as the high and anisotropic carrier mobility, can facilitate the photo-generated carrier separation to improve the photoelectric conversion process. In contrast to the M 2 CO 2 and MoX 2 monolayers, the M 2 CO 2 /MoX 2 heterostructures display a heightened optical absorption effect, predominantly within the ultraviolet and visible light spectra. Interestingly, the M 2 CO 2 /MoX 2 heterostructures all exhibit the intrinsic type-II semiconductors, the VBM and CBM primarily influenced by the contribution of different layers, which effectively hinder the recombination of electron-hole pairs. Lastly, the Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures are considered highly prospective contenders for water splitting, given their appropriate band gaps and band edge positions that furnish ample driving force for the redox reaction of water. Furthermore, the designed Hf 2 CO 2 /MoS 2 and Zr 2 CO 2 /MoS 2 heterostructures can achieve PCE values of 19.75% and 17.13%, respectively. The present study reveals that M 2 CO 2 /MoX 2 vdW heterostructures are potential candidates for photocatalytic and photovoltaic device applications.
Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/molecules28083525/s1, Figure S1. The projected band structure of (a) MoS 2 , (b) MoSe 2 , (c) MoTe 2 , (d) Zr 2 CO 2 , (e) Hf 2 CO 2 monolayers. (f) The first Brillouin zone and high symmetry points of the hexagonal 2D lattice; Figure S2. An orthorhombic lattice instead of the traditional hexagonal lattice was adopted to calculate the intrinsic responses to uniaxial strain in the Zr 2 CO 2 /MoS 2 heterostructure; Figure S3. Different adsorption sites of the water molecule on the (a) Zr 2 CO 2 and (b) Hf 2 CO 2 surfaces of the Zr 2 CO 2 /MoSe 2 and Hf 2 CO 2 /MoSe 2 heterostructures; Figure S4. Optimized structures and adsorption energies of the water molecule with H as the adsorption atom at (a) A, (b) B, (c) C adsorption site and O as the adsorption atom at (d) A, (e) B, (f) C adsorption site on the Zr 2 CO 2 surface of the Zr 2 CO 2 /MoSe 2 heterostructure; Figure S5. Optimized structures and adsorption energies of the water molecule with H as the adsorption atom at (a) D, (b) E, (c) F adsorption site and O as the adsorption atom at (d) D, (e) E, (f) F adsorption site on the Hf 2 CO 2 surface of the Hf 2 CO 2 /MoSe 2 heterostructure; Figure S6. The HSE06 band structures of mutually independent monolayers fixed in the heterostructure lattices for (a) Hf 2 CO 2 /MoS 2 , (b) Hf2CO 2 /MoSe 2 , (c) Hf 2 CO 2 /MoTe 2 , (d) Zr 2 CO 2 /MoS 2 , (e) Zr 2 CO 2 /MoSe 2 and (f) Zr 2 CO 2 /MoTe 2 ; Table S1. The lattice constants a (Å), band gaps E g (eV) and band gap types of M 2 CO 2 (M = Zr, Hf) and MoX 2 (X = S, Se, Te) monolayers; Table S2. The total energy (eV) of different stacking configurations for M 2 CO 2 /MoX 2 heterostructures; Table S3. The lattice constants a (Å), interlayer distance d (Å), degree of lattice mismatch K, formation energy E f (meV) and binding energy E b (meV/Å 2 ) for the most stable configurations of M 2 CO 2 /MoX 2 heterostructures; Table S4. The calculated band gap E g (eV) of the most stable configurations for M 2 CO 2 /MoX 2 heterostructures; Table S5. The total charge transfer amounts between MoX 2 and M 2 CO 2 in the M 2 CO 2 /MoX 2 heterostructures; Table S6. The conduction band offset ∆E c (eV), donor band gap E d g (eV), and calculated power conversion efficiency (PCE) η (%) of M 2 CO 2 /MoX 2 heterostructures for solar cell applications. References [56][57][58][59][60][61][62][63] are cited in the supplementary materials.